On a perturbed Dirichlet problem for a nonlocal differential equation of Kirchhoff type.
On a semilinear elliptic equation in
We prove existence/nonexistence and uniqueness of positive entire solutions for some semilinear elliptic equations on the Hyperbolic space.
On Kirchhoff type problems involving critical and singular nonlinearities
In this paper, we are interested in multiple positive solutions for the Kirchhoff type problem ⎧ in Ω ⎨ ⎩ u = 0 on ∂Ω, where Ω ⊂ ℝ³ is a smooth bounded domain, 0∈Ω, 1 < q < 2, λ is a positive parameter and β satisfies some inequalities. We obtain the existence of a positive ground state solution and multiple positive solutions via the Nehari manifold method.
On multiple solutions of concave and convex nonlinearities in elliptic equation on .
On the elliptic problems involving multisingular inverse square potentials and concave-convex nonlinearities.
On the existence of five nontrivial solutions for resonant problems with p-Laplacian
In this paper we study a nonlinear Dirichlet elliptic differential equation driven by the p-Laplacian and with a nonsmooth potential. The hypotheses on the nonsmooth potential allow resonance with respect to the principal eigenvalue λ₁ > 0 of . We prove the existence of five nontrivial smooth solutions, two positive, two negative and the fifth nodal.
On the existence of multiple positive solutions for a certain class of elliptic problems
We investigate the existence of solutions for the Dirichlet problem including the generalized balance of a membrane equation. We present a duality theory and variational principle for this problem. As one of the consequences of the duality we obtain some numerical results which give a measure of a duality gap between the primal and dual functional for approximate solutions.
On the Neumann problem for systems of elliptic equations involving homogeneous nonlinearities of a critical degree
We establish the existence of solutions for the Neumann problem for a system of two equations involving a homogeneous nonlinearity of a critical degree. The existence of a solution is obtained by a constrained minimization with the aid of P.-L. Lions' concentration-compactness principle.